In order to describe a conventional technique, first, the basic fuzzy inference will be outlined by taking as an example fuzzy control used in apparatus control, etc.
In a control system which relates to the evaluation of human beings, the operator can determine a final manipulated control variable using a variable which the operator has determined subjectively and/or sensuously, for example, "large", "middle", "tremendously", or "a little" (which is hereinafter referred to as a fuzzy variable). In this case, the operator determines the manipulated variable from the input variables on the basis of his control experience. An inference device using fuzzy control assigns an input fuzzy number to an IF part of an inference rule in accordance with the inference rule of "IF . . . THEN . . ." type and determines an output fuzzy number of the THEN part from a fitting grade (membership value) indicative of the extent to which the inference rule is satisfied. The actual manipulated variable can be obtained by taking the center of gravity value, etc., of the output fuzzy number.
One of the conventional control methods using fuzzy inference is fuzzy modeling disclosed, for example, in Gean-Taek Kang, Michio Sugano; "fuzzy modeling" SOCIETY OF INSTRUMENT AND CONTROL ENGINEERS PAPERS, Vol. 23, No. 6, pp. 650-652, 1987. In the control rule of the fuzzy modeling, the IF part is constituted by a fuzzy proposition and the THEN part is constituted by a regular linear equation between inputs and outputs. If a timing lag of first order tank model is considered, for example, the control rule among a control error e, its change in error de and a control output (manipulated variable) u is given by
If e is Zero and de is Positive Medium PA1 Then u=0.25 e+1.5 de
A plurality of such inference rules are prepared, all of which are referred to as control rules. Zero, Positive Medium, etc., are each a label or a fuzzy variable (fuzzy number) used to described the rules. FIG. 1 illustrates one example of a fuzzy variable. In FIG. 1, NB denotes Negative Big; NM, a negative Medium; NS, a Negative Small; ZO, a Zero; PS, Positive Small; PM, a Positive Medium; and PB, Positive Big. A function indicative of a fuzzy number F on X is referred to as a membership function .mu..sub.f ( ) and the function value of x.sup.0 is referred to as a membership value .mu..sub.F (X.sup.0). The general form of the control rules is given by EQU R.sup.s : If x.sub.1 is A.sub.1.sup.s, x.sub.2 is A.sub.2.sup.s, . . . , x.sub.m is A.sub.m.sup.s EQU Then y.sup.s =c.sub.0.sup.s +c.sub.1.sup.s x.sub.1 +c.sub.2.sup.s x.sub.2 +. . . +c.sub.m.sup.s x.sub.m
where R.sup.5 indicates a s.sup.th rule; x.sub.j, an input variable; A.sub.j.sup.s, a fuzzy variable; y.sup.s, an output from the s.sup.th rule; and c.sup.s, a THEN part parameter. The result of inference for an input (x.sub.1.sup.0, x.sub.2.sup.0, . . . , x.sub.m.sup.0) is given by ##EQU1## where n is the number of rules, and w.sup.s is a fitting grade at which the input (x.sub.1.sup.0, x.sub.2.sup.0, . . . , x.sub.m.sup.0) is adapted to the IF part of the S.sup.th rule. W.sup.s is given by ##EQU2## where the membership value in the x.sup.0 in the fuzzy variable A.sub.j.sup.s is .mu..sub.Aj.sup.s (x.sub.j). The identification of a fuzzy model includes a two-stage structure, namely, identification of the structure of the IF and THEN parts and identification of the IF and THEN parts. The conventional identifying process includes the steps of (1) changing the fuzzy proposition of the IF part to a proper proposition, (2) changing W.sup.s in a constant manner, (3) searching only the actually required ones of the input variables of the THEN part using a backward elimination method, (4) calculating parameters of the THEN part using the method of least squares, (5) repeating the steps (2)-(4) to determine an optimal parameter, (6) changing the fuzzy proposition of the IF part and (7) returning to the step (2) where an optimal parameter is repeatedly searched under the conditions of a new fuzzy proposition. Namely, this method can be said to be a heuristic method-like identifying algorithm.
A conventional inference device includes a fuzzy inference device, for example, shown in FIG. 2 in which reference numeral 1a denotes a data input unit (including a measured value and a value evaluated by human being); 2a, a display command unit; 3a, a fuzzy inference operation unit; 4a, an inference result output unit; and 5a, a display. The display 2a is composed of a keyboard, and the fuzzy inference operation unit 3a is composed of a digital computer. The input data to the digital input unit 1a is subjected to inference operation at the fuzzy inference operation unit 3a. Thus, the operation unit 3a outputs the result of the inference and simultaneously displays a list of inference rules, a list of fuzzy variables and the states of use of various inference rules on the display 5a. In a conventional inference device such as that shown in FIG. 2, the inference rules of the fuzzy inference rules and the fuzzy variables as input data are fixed as constant values in the fuzzy inference operation unit 3a and have no function of changing the fuzzy variables.
Since an algorithm of determining a membership function is based on heuristic method in the conventional inference rule determining method as well as in the fuzzy modeling, it is complicated and the number of parameters to be determined is very large. Therefore, optimal inference rules cannot be obtained easily at high speed.
Since an influence device such as that shows in FIG. 2 has no function of learning inference rules, the characteristic of the inference variable changes with time, so that it cannot cope with the situation that the inference accuracy would be deteriorated according to the inference rules set initially. Assume, for example, that there is the inference rule "If it is hot, then control diarie a so as to be in level B." Since the obscure concept "hot" varies from person to person as well as season to season, satisfactory control cannot be achieved unless the inference device has a learning function and can change the inference rules adaptively in accordance with situations under which the device is used. Furthermore, there are actually many cases where non-linear inference is required, so that a method of performing linear approximation described with reference to the above conventional example has a limit to improvement in the inference accuracy.